We have carried out measurements of domain wall dynamics in a Pt/Co/GdOx(t) wedge sample with perpendicular magnetic anisotropy. When driven by an easy-axis field Hz in the presence of an in-plane field Hx, the domain wall expansion along x is anisotropic, as expected for samples presenting Dzyaloshinskii-Moriya interaction. In the creep regime, the sign and the value of the domain wall velocity asymmetry changes along the wedge. We show that in our samples the domain wall speed vs. Hx curves in the creep regime cannot be explained simply in terms of the variation of the domain wall energy with Hx, as suggested by previous works. For this reason the strength and the sign of the Dzyaloshinskii-Moriya interaction (DMI) cannot be extracted from these measurements. To obtain reliable information on the DMI strength using magnetic field-induced domain wall dynamics, measurements have been performed with high fields, bringing the DW close to the flow regime of propagation. In this case, the large values of DMI are coherent with those obtained from current-driven domain wall dynamics. ; Comment: 12 pages, 5 figures